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The parametric coordinate of any point of the parabola y2 = 4ax is
1. (at², 2at)
2. (-at², 2at) 
3. (a sin2 t, -2a sin t)
4. None of these

1 Answer

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Best answer
Correct Answer - Option 1 : (at², 2at)

Calculation:

Parabola

Parametric
equation

y2 = 4ax (at2, 2at)
y2 = -4ax (-at2, 2at)
x2 = +4ay (2at, at2)
x2 = -4ay (2at, -at2)
(y - k2) = 4a(x - h) (h + at2, k + 2at)
(y - p2) = 4b(y - q) (p + 2at, q + at2)

Here, the given parabola is y2 = 4ax

So, its parametric coordinate is (at², 2at)

We can check it by putting the above point in the equation of parabole 

L.H.S = y2

⇒ (2at)2

⇒ 4a2t2     -----(i)

R.H.S = 4ax

⇒ 4 × a × at2

⇒ 4a2t2     -----(ii)

From (i) and (ii), we get 

∴ (at², 2at) is the parametric coordinates of the parabola y = 4ax.

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